Skip to main content
SpringerLink
Log in

A new construction of Riemann surfaces with corona

  • Published:
The Journal of Geometric Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ailing, N. A proof of the corona conjecture for finite open Riemann surfaces,Bull. Amer. Math. Soc,70, 110–112, (1964).

    Article  MathSciNet  Google Scholar 

  2. Barrett, D. and Diller, J. Contraction properties of the Poincaré series operator,Michigan Math. J.,43, 519–538, (1996).

    Article  MathSciNet  MATH  Google Scholar 

  3. Carleson, L. Interpolations by bounded analytic functions and the corona problem,Annals of Math.,76, 547–559, (1962).

    Article  MathSciNet  Google Scholar 

  4. Diller, J. A canonical\(\bar \partial \) problem for bordered Riemann surfaces,Indiana Univ. Math. J.,44, 747–763, (1995).

    Article  MathSciNet  MATH  Google Scholar 

  5. Diller, J. Limits on an extension of Carleson’s\(\bar \partial - theorem\),J. Geometric Anal.,6, 1–17, (1996).

    MathSciNet  MATH  Google Scholar 

  6. Forster, O.Lectures on Riemann Surfaces, Springer-Verlag, Berlin, 1981.

    MATH  Google Scholar 

  7. Gamelin, T.Uniform Algebras and Jensen Measures, London Math. Soc., Lecture Note Series # 32, 1978.

  8. Garnett, J.B.Bounded Analytic Functions, Academic Press, New York, 1981.

    MATH  Google Scholar 

  9. Garnett, J.B.Analytic Capacity and Measure, Springer-Verlag, Lecture Notes in Mathematics # 297, 1972.

  10. Gamett, J.B. and Jones, P.W. The corona theorem for Denjoy domains,Acta Math.,155, 27–40, (1985).

    Article  MathSciNet  Google Scholar 

  11. Hörmander, L.An Introduction to Complex Analysis in Several Variables, 3rd ed., North-Holland, 1990.

  12. Hubbard, J.H. and Papadopol, P. Superattractive fixed points in ℂn,Indiana Univ. Math. J.,43, 321–365, (1994).

    Article  MathSciNet  MATH  Google Scholar 

  13. McMullen, C. Amenable coverings of complex manifolds and holomorphic probability measures,Invent. Math.,110, 29–37, (1992).

    Article  MathSciNet  MATH  Google Scholar 

  14. Moore, C. The corona theorem for domains whose boundary lies in a smooth curve,Proc. Amer. Math. Soc,100, 266–270, (1987).

    Article  MathSciNet  MATH  Google Scholar 

  15. Ransford, T.J. Variation of Hausdorff dimension of Julia sets,Ergodic Theor. Dynamical Syst.,13, 167–179, (1993).

    MathSciNet  MATH  Google Scholar 

  16. Stout, E.L. Bounded holomorphic functions on finite Riemann surfaces,Trans. Amer. Math. Soc.,120, 255–285, (1965).

    Article  MathSciNet  Google Scholar 

  17. Tsuji, M.Potential Theory in Modern Function Theory, Maruzen, 1959.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 525 E. University Avenue, 48109-1109, Ann Arbor, MI

    David E. Barrett

  2. Department of Mathematics, University of Notre Dame, Room 370, 46556-5683, CCMB Notre Dame, IN

    Jeffrey Diller

Authors
  1. David E. Barrett
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeffrey Diller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David E. Barrett.

Additional information

Communicated by John Fornæss

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barrett, D.E., Diller, J. A new construction of Riemann surfaces with corona. J Geom Anal 8, 341–347 (1998). https://doi.org/10.1007/BF02921790

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02921790

Math Subject Classifications

Search

Navigation